My experience with the WBBB (relative to the wrapping/cocooning concern) is that the zipper side pullout does a very good job of "opening up" that side of the hammock (by your head in a diagonal lay). After trial and error, I note that the further "out" the side pullout goes (more horizontal; more distance away from the hammock for a staking point), the more effective it is at doing its job.
+1 on your need for a side zipper!
"The more I carry the happier I am in camp; the less I carry the happier I am getting there" - Sgt. Rock